Question

please help in these method 8 question

Answer 1

1/

Solution:

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Given:

$3^{-7}$÷$3^{-10} = 3^{2m-1}$

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To Find;

The value of m,.

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We know that,

if we have the same base number and different exponents in division,

We should subtract the power,.

=> $3^{-7 -(-10)} = 3^{2m-1}$

=> $3^{-7 + 10} = 3^{2m-1}$

=> $3^{3} = 3^{2m-1}$

=> $\frac{3^{3}}{3^{2m-1}} = 1$

Again, it is in division, so,.

=> $3^{3- (2m-1)} = 1$

We know that,

anything power 0 is 1,.So,

=> $3^{3 - 2m + 1} = 3^{0}$

=> $3 - 2m + 1 = 0$ (In exponents,.)

=> 4 - 2m = 0

=> 4 = 2m

=> m = $\frac{4}{2}$

=> m = 2,.

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2/

Solution :

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Given :

$( \frac{1}{4} )^{3m} ( \frac{1}{4} )^2 = ( \frac{1}{4} )^{m - 6}$

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To find :

The value of m,.

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As we know (we did in previous problem),

In multiplication of numbers with same base with different exponents,

we need to add the powers,.

=> $( \frac{1}{4} )^{3m + 2} = ( \frac{1}{4})^{m-6}$

=> 3m + 2 = m - 6

=> 3m - m = -6 + 2

=> 2m = -4

=> $m = \frac{-4}{2}$ = -2

∴ m = -2,.

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